Capturing a phylogenetic tree when the number of character states varies with the number of leaves

Mike Steel

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arXiv · 1503.00831

Capturing a phylogenetic tree when the number of character states varies with the number of leaves

Mike Steel

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Abstract

We show that for any two values $\alpha, \beta >0 $ for which $\alpha+\beta>1$ then there is a value $N$ so that for all $n \geq N$ the following holds. For any binary phylogenetic tree $T$ on $n$ leaves there is a set of $\lfloor n^\alpha \rfloor$ characters that capture $T$, and for which each character takes at most $\lfloor n^\beta \rfloor$ distinct states. Here `capture' means that $T$ is the unique perfect phylogeny for these characters. Our short proof of this combinatorial result is based on the probabilistic method.

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Mike Steel. 2015-03-03. Capturing a phylogenetic tree when the number of character states varies with the number of leaves. https://arxiv.org/abs/1503.00831

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